The * operator works component-wise for vectors like vec4.
vec4 a = vec4(1.0, 2.0, 3.0, 4.0);
vec4 b = vec4(0.1, 0.2, 0.3, 0.4);
vec4 c = a * b; // vec4(0.1, 0.4, 0.9, 1.6)
The GLSL Language Specification says under section 5.10 Vector and Matrix Operations:
With a few exceptions, operations are component-wise. Usually, when an
operator operates on a vector or matrix, it is operating independently
on each component of the vector or matrix, in a component-wise
fashion. […] The exceptions are matrix multiplied by vector, vector
multiplied by matrix, and matrix multiplied by matrix. These do not
operate component-wise, but rather perform the correct linear
algebraic multiply.